Learning Confidence Bounds for Classification with Imbalanced Data

Class imbalance poses a significant challenge in classification tasks, where traditional approaches often lead to biased models and unreliable predictions. Undersampling and oversampling techniques have been commonly employed to address this issue, yet they suffer from inherent limitations stemming from their simplistic approach such as loss of information and additional biases respectively. In this paper, we propose a novel framework that leverages learning theory and concentration inequalities to overcome the shortcomings of traditional solutions. We focus on understanding the uncertainty in a class-dependent manner, as captured by confidence bounds that we directly embed into the learning process. By incorporating class-dependent estimates, our method can effectively adapt to the varying degrees of imbalance across different classes, resulting in more robust and reliable classification outcomes. We empirically show how our framework provides a promising direction for handling imbalanced data in classification tasks, offering practitioners a valuable tool for building more accurate and trustworthy models.

Tighter Variational Representations of f-Divergences via Restriction to Probability Measures

We show that the variational representations for f-divergences currently used in the literature can be tightened. This has implications to a number of methods recently proposed based on this representation. As an example application we use our tighter representation to derive a general f-divergence estimator based on two i.i.d. samples and derive the dual program for this estimator that performs well empirically. We also point out a connection between our estimator and MMD.